Introducing radio communication systems with highly-advanced transfer schemes have been actively studied in recent years. Examples of the studied radio communication systems are multi-antenna transmission using a plurality of transmission antennas, and CoMP (Coordinated Multi-Point transmission and reception) in which data destined for the same mobile station device is transmitted in a coordinated manner using a plurality of base stations or transmission points.
When one data is transmitted using a plurality of transmission antennas, a precoding technique is employed to keep transmission signals, transmitted from the individual transmission antennas, in the same phase at the time of reception. In the LTE (Long Term Evolution) system of which service has started from December, 2010, for example, the multi-antenna transmission is realized by selecting an index (PMI: Precoding Matrix Indicator) of one among a set of predefined precoding matrices, which one provides maximum performance, and by feeding back the selected PMI from a mobile station device to a base station device (see Non Patent Literature (NPL) 1). Theoretically, a right singular vector corresponding to a maximum singular value among plural singular values, including the case of one singular value, obtained with SVD (Singular Value Decomposition) of a channel matrix between the mobile station device and the base station device is regarded to be optimum as a precoding matrix. For example, the Singular Value Decomposition is expressed by the following formula (a1).H=UVDH  (a1)
In the above formula, U and V are Unitary matrices of which inverse matrices are adjoint matrices thereof, and which have a size of the number of reception antennas×the number of reception antennas and a size of the number of transmission antennas×the number of transmission antennas, respectively. D is called a singular value matrix, i.e., a matrix having singular values as diagonal elements, and D is a diagonal matrix having a size of the number of reception antennas×the number of transmission antennas. H is a channel matrix of complex numbers for a channel between the base station device and the mobile station device, and H has a size of the number of reception antennas×the number of transmission antennas. The channel matrix H is expressed by the following formula (a2).
                    H        =                  [                                                                      H                  11                                                            …                                                              H                                      1                    ⁢                                          N                      t                                                                                                                          ⋮                                            ⋱                                            ⋮                                                                                      H                                                            N                      r                                        ⁢                    1                                                                              …                                                              H                                                            N                      r                                        ⁢                                          N                      t                                                                                                    ]                                    (                  a          ⁢                                          ⁢          2                )            
In the above formula, Nr denotes the number of reception antennas, and Nt denotes the number of transmission antennas. Hnm denotes a channel characteristic between an m-th transmission antenna and an n-th reception antenna, and it is expressed by complex numbers.
The CoMP is described below. In the CoMP, points transmitting the same data are geographically apart from one another. Although a technique similar to that in the above-described multi-antenna transmission can be used, the transmission is performed while synchronism is established among the transmitting points on condition that channel information (or information related to a precoding matrix, such as the PMI) and transmission data are shared among all the transmitting points (see NPL 2). The term “synchronism” used here implies that a deviation in carrier frequency is small among base stations, and that reception timings at which mobile station devices receive the transmission data are matched with each other.